The age of mother is four times as much as the sum of the age of her three childern but 4 years hence her age will be only double the sum of their ages. Find age of mother? ( in years )

40

ATQ,

At present ratio of age of mother to sum of age of three children = 4 : 1

4 years hence ratio of age of mother to sum of age of three children = 2 : 1

ATQ,

⇒ \(\frac{4R+4}{1R + 12}\) = \(\frac{2}{1}\)

⇒ 4R + 4 = 2R + 24

⇒ 2R = 20

⇒ 1R = 10

present age of mother = 4 × 10 = 40

*(added 12 years because 1R is the sum of age of three children and after 4 years total sum increase by 12 years)